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UNO [17]
3 years ago
7

the sum of the first three terms of a sequence Is 42 The fourth term is 24. find u1 and the common difference

Mathematics
1 answer:
e-lub [12.9K]3 years ago
6 0

10=2d

Given:

The sum of the first three terms of a sequence Is 42.

The fourth term is 24.

To find:

The  u₁ and the common difference

Step-by-step explanation:

nth term of a sequence is

u_n=u_1+(n-1)d

where, u₁ is first term and d is common difference.

4th term is 24.

u_4=u_1+(4-1)d

24=u_1+3d           ...(i)

Sum of nth term of an AP is

S_n=\dfrac{n}{2}[2u_1+(n-1)d]

Sum of first three terms is 42.

S_3=\dfrac{3}{2}[2u_1+(3-1)d]

42=\dfrac{3}{2}[2u_1+2d]

Divide both sides by 3.

14=u_1+d          ...(ii)

On subtract (ii) from (i), we get

10=2d

5=d

Put d=5 in equation (ii).

14=u_1+5

14-5=u_1

9=u_1

Therefore, the first term is u_1=9 and common difference is d=5 .

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